
where \(\tilde{x}_S^{(k,i)}\)  with \(k \in \lbrace 1,\ldots ,l\rbrace \)  is the \(k\) -th sample of \(x_S\)  for the \(i\) -th observation.
For the marginal PFI, \(\tilde{x}_{S}^{(k,i)}\)  can be a permutation of the original vector \(x_S\) .
The conditional PFI requires a conditional sampling mechanism for the feature, such as subgroups [1]} or knockoffs [2]}, [3]}.
The estimation of \(\widehat{PFI}\)  requires unseen data, so that the loss estimates deliver unbiased results [4]}, [5]}.
If not stated otherwise, mathematical derivations in this paper apply to both marginal and conditional PFI.
We assume that the loss used for PFI can be computed per instance, which excludes losses such as AUC.
See Figure REF  for a PFI example.
As with PD, we use \(PFI\)  instead of \(PFI_S\)  and \(\widehat{PFI}\)  instead of \(\widehat{PFI}_S\) s.
